Full movie description "Leave It to Beaver My Brother's Girl":

Wally's class is having a dance. Wally is going, but like most of the other boys in the class, he isn't going to ask a girl to go with him. Instead, he plans on hanging out with Eddie Haskell and some of the other boys. On the other hand, the girls in the class lament that none of the boys are asking any of them to go. Mary Ellen Rogers believes she's figured out a way for Wally to take her to the dance. Her plan includes using the Beaver without his knowledge and befriending him with the use of her father's electric train set. As Mary Ellen progresses with her plan, it becomes the battle of the sexes, even in the Cleaver household, with June understanding why Mary Ellen would need to resort to such underhanded measures. In the end, Beaver may be the one who gets hurt.

Reviews of the Leave It to Beaver My Brother's Girl

A cute and poignant episode from the first season. Beaver briefly
becomes a go-between in order to facilitate a dance date between Wally
and Mary Ellen Rogers. He learns a bitter lesson about feminine wiles
when he realizes that Mary Ellen was simply "using" him. Wally is just
on the cusp of developing an interest in girls, but is not quite there
yet. A number of different viewpoints are highlighted in the episode:
Ward has a man-to-man talk with Beaver about women; June then breaks in
and offers her point of view. And we get to see what a poised young
actress Pamela Baird (who played Mary Ellen Rogers) was. Altogether, a
superlative first-season episode.